Demodulation of DSB-SC AM Signals

1
Demodulation of DSB-SC AM Signals

• Suppose that the DSB-SC AM signal u(t) is
  transmitted through an ideal channel (with no
  channel distortion and no noise)
• Then the received signal is equal to the
  modulated signal,
• Suppose we demodulate the received signal by
• Multiplying r(t) by a locally generated sinusoid
  cos(2?fct ?).
• We pass the product signal through an ideal
  lowpass filter with bandwidth W

2
Demodulation of DSB-SC AM Signals

• The multiplication of r(t) with cos(2?fct ?)
  yields
• 
  
• Since the frequency content of m(t) is limited
  to W Hz, where
• W ltlt fc, the lowpass filter can be designed
  to eliminate the signal components centered at 2
  fc and to pass the signal components centered at
  f 0

Frequency-domain representation of the DSB-SC AM
demodulation.
3
Demodulation of DSB-SC AM Signals

• Consequently, the output of the ideal lowpass
  filter
• Note that m(t) is multiplied by cos(?)
• So the power in the demodulated signal is
  decreased by a factor of cos2?
• Thus, the desired signal is scaled in amplitude
  by a factor that depends on the phase ? of the
  locally generated sinusoid
• When ? ? 0, the amplitude of the desired signal
  is reduced by the factor cos(?)
• If ? 45?, the amplitude of the signal is
  reduced by and the power is reduced by a
  factor of two
• If ? 90?, the desired signal component vanishes

4
Demodulation of DSB-SC AM Signals

• The preceding discussion demonstrates the need
  for a phase-coherent or synchronous demodulator
  for recovering the message signal m(t) from the
  received signal
• That is, the phase ? of the locally generated
  sinusoid should ideally be equal to 0 (the phase
  of the received-carrier signal)
• A sinusoid that is phase-locked to the phase of
  the received carrier can be generated at the
  receiver in one of two ways

5
Demodulation of DSB-SC AM Signals

• One method is to add a carrier component into the
  transmitted signal.
• We call such a carrier component "a pilot tone."
• Its amplitude Ap is selected to be significantly
  smaller than those of the modulated signal u(t).
• Thus, the transmitted signal is a
  double-sideband, but it is no longer a suppressed
  carrier signal

Addition of a pilot tone to a DSB-AM signal.
6
Demodulation of DSB-SC AM Signals

• At the receiver, a narrowband filter tuned to
  frequency fc, filters out the pilot signal
  component
• Its output is used to multiply the received
  signal, as shown in below
• We may show that the presence of the pilot signal
  results in a DC component in the demodulated
  signal
• This must be subtracted out in order to recover
  m(t)

Use of a pilot tone to demodulate a DSB-AM
signal.
7
Demodulation of DSB-SC AM Signals

• Adding a pilot tone to the transmitted signal has
  a disadvantage
• It requires that a certain portion of the
  transmitted signal power must be allocated to the
  transmission of the pilot
• As an alternative, we may generate a
  phase-locked sinusoidal carrier from the received
  signal r(t) without the need of a pilot signal
• This can be accomplished by the use of a
  phase-locked loop, as described in Section 6.4.

8
Conventional Amplitude Modulation

• A conventional AM signal consists of a large
  carrier component, in addition to the
  double-sideband AM modulated signal
• The transmitted signal is expressed as
• The message waveform is constrained to satisfy
  the condition that m(t) ? 1
• We observe that Acm(t) cos(2?fct) is a
  double-sideband AM signal and Accos(2?fct) is the
  carrier component

A conventional AM signal in the time domain
9
Conventional Amplitude Modulation

• As we will see later in this chapter, the
  existence of this extra carrier results in a very
  simple structure for the demodulator
• That is why commercial AM broadcasting generally
  employs this type of modulation
• As long as m(t) ? 1, the amplitude Ac1 m(t)
  is always positive
• This is the desired condition for conventional
  DSB AM that makes it easy to demodulate, as we
  will describe
• On the other hand, if m(t) lt -1 for some t , the
  AM signal is overmodulated and its demodulation
  is rendered more complex

10
Conventional Amplitude Modulation

• m(t) is scaled so that its magnitude is always
  less than unity
• It is convenient to express m(t) as
• where m,(t) is normalized such that its minimum
  value is -1 and
• The scale factor a is called the modulation
  index, which is generally a constant less than 1
• Since m(t) ? 1 and 0 lt a lt 1, we have 1 amn(
  t ) gt 0 and the modulated signal can be expressed
  as
• which will never be overmodulated

11
Spectrum of the Conventional AM Signal

• The spectrum of the amplitude-modulated signal
  u(t) is
• Obviously, the spectrum of a conventional AM
  signal occupies a bandwidth twice the bandwidth
  of the message signal

Conventional AM in both the time and frequency
domain.
12
Power for the Conventional AM Signal

• A conventional AM signal is similar to a DSB when
  m(t) is substituted with 1 amn(t)
• DSB-SC The power in the modulated signal
• where Pm denotes the power in the message signal
• Conventional AM
• where we have assumed that the average of mn(t)
  is zero
• This is a valid assumption for many signals,
  including audio signals.

13
Power for the Conventional AM Signal

• Conventional AM,
• The first component applies to the existence of
  the carrier, and this component does not carry
  any information
• The second component is the information-carrying
  component
• Note that the second component is usually much
  smaller than the first component (a lt 1, mn(t)
  lt 1, and for signals with a large dynamic range,
  Pmn ltlt 1)
• This shows that the conventional AM systems are
  far less power efficient than the DSB-SC systems
• The advantage of conventional AM is that it is
  easily demodulated

14
Demodulation of Conventional DSB-AM Signals

• The major advantage of conventional AM is the
  ease in which the signal can be demodulated
• There is no need for a synchronous demodulator
• Since the message signal m(t) satisfies the
  condition m(t) lt 1, the envelope (amplitude)
  1m (t) gt 0
• If we rectify the received signal, we eliminate
  the negative values without affecting the message
  signal, as shown in below
• The rectified signal is equal to u(t) when u(t) gt
  0, and zero when u(t) lt 0
• The message signal is recovered by passing the
  rectified signal through a lowpass filter whose
  bandwidth matches that of the message signal
• The combination of rectifier and lowpass filter
  is called an envelope detector

15
Demodulation of Conventional DSB-AM Signals

• The output of the envelope detector is of the
  form
• where gl represents a DC component and g2 is a
  gain factor due to the signal demodulator.
• The DC component can be eliminated by passing
  d(t) through a transformer, whose output is
  g2m(t).
• The simplicity of the demodulator has made
  conventional DSB-AM a practical choice for
  AM-radio broadcasting
• Since there are billions of radio receivers, an
  inexpensive implementation of the demodulator is
  extremely important
• The power inefficiency of conventional AM is
  justified by the fact that there are few
  broadcast transmitters relative to the number of
  receivers
• Consequently, it is cost-effective to construct
  powerful transmitters and sacrifice power
  efficiency in order to simplify the signal
  demodulation at the receivers